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Three particles, each of the mass m are ...

Three particles, each of the mass `m` are situated at the vertices of an equilateral triangle of side `a`. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original mutual separation `a`. Find the initial velocity that should be given to each particle and also the time period of the circular motion. `(F=(Gm_(1)m_(2))/(r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A
`F_(A) = F _(AB) +F_(AC)`
`= 2[(Gm^(2))/(a^(2))]cos30^(@) = sqrt 3[(Gm^(2))/(a^(2))]`
`r = (a)/(sqrt3)`,
`(m upsilon^(2))/(r) = F` or `(sqrt3m upsilon ^(2))/(a) = (sqrt3Gm^(2))/(a)`
`upsilon = sqrt ((Gm)/(a))`.
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